标准线性固体材料中球面应力波传播特征研究

Characteristics of spherical stress wave propagation in the standard linear solid material

基于标准线性固体模型,结合球面波波动方程,给出了球面应力波的粒子速度v、粒子位移u、径向应力σr、切向应力σθ、径向应变εr、切向应变εθ、折合速度势、折合位移势在Laplace域的理论解.采用基于Crump算法的Laplace数值逆变换方法分析了上述物理量的传播特征.Laplace数值反演结果表明,线黏弹性材料对强间断球面应力波的初始响应为纯弹性响应,强间断在传播过程中包含了几何衰减和本构黏性衰减,应力、应变、粒子速度的衰减特性和粒子位移、应力、应变、折合位移势等物理量的稳态值同黏弹性球面波的理论预测一致.折合速度势和折合位移势的峰值随波传播距离的增加逐渐衰减,这与理想弹性理论给出的折合速度势和折合位移势不随传播距离变化的结论不同.折合位移势的稳态值与介质的静态剪切模量成反比,与稳态空腔压力成正比,与空腔半径的三次方成正比.

Based on the standard linear solid model, the solutions in Laplace domain, such as particle velocity ν, particle displacement u, radial stress σt, tangential stress ae, radial strain εr, tangential strain εθ, reduced velocity potential γ（RVP）, and reduced displacement potential ψ （RDP）, are derived from the spherical wave equations. The propagating characteristics of these physical quantities, as mentioned above, are calculated by using Crump algorithm for inverse Laplace transformation. The numerical inversion results reveal that the initial response to strong discontinuity spherical stress wave in viscoelastic material is purely elastic response. The strong discontinuities, such as σr, σθ, εr, εθ and v, contain geometrical attenuation and viscoelastic damping in the process of wave propagation. The variables, such as σr, σθ, εr, εθ , u and ψ, converge to steady values as time approaches to infinity. The peak values of RVP γ and RDP ψ, which are constant in a purely elastic material, are steadily reduced with the spreading distance increasing in viscoelastic material. The steady values of ψ are in inverse relation to the static shear modulus Ga and directly proportional to the steady cavity pressure and the cube of the cavity radius r.